Question
Which value of x satisfies the equation start fraction, 2, divided by, 3, end fraction, left parenthesis, x, minus, start fraction, 3, divided by, 2, end fraction, right parenthesis, equals, one third
3
2
(x−
2
3
)=
3
1
?
3
2
(x−
2
3
)=
3
1
?
Answers
GPT-4o mini
To solve the equation
\[
\frac{2}{3} \left( x - \frac{3}{2} \right) = \frac{1}{3},
\]
we will first eliminate the fraction on the left side by multiplying both sides of the equation by 3:
\[
3 \cdot \left( \frac{2}{3} \left( x - \frac{3}{2} \right) \right) = 3 \cdot \frac{1}{3}.
\]
This simplifies to:
\[
2 \left( x - \frac{3}{2} \right) = 1.
\]
Next, divide both sides by 2:
\[
x - \frac{3}{2} = \frac{1}{2}.
\]
Now, to isolate \( x \), we add \( \frac{3}{2} \) to both sides:
\[
x = \frac{1}{2} + \frac{3}{2}.
\]
Combining these fractions, we have:
\[
x = \frac{1 + 3}{2} = \frac{4}{2} = 2.
\]
Thus, the value of \( x \) that satisfies the equation is:
\[
\boxed{2}.
\]
\[
\frac{2}{3} \left( x - \frac{3}{2} \right) = \frac{1}{3},
\]
we will first eliminate the fraction on the left side by multiplying both sides of the equation by 3:
\[
3 \cdot \left( \frac{2}{3} \left( x - \frac{3}{2} \right) \right) = 3 \cdot \frac{1}{3}.
\]
This simplifies to:
\[
2 \left( x - \frac{3}{2} \right) = 1.
\]
Next, divide both sides by 2:
\[
x - \frac{3}{2} = \frac{1}{2}.
\]
Now, to isolate \( x \), we add \( \frac{3}{2} \) to both sides:
\[
x = \frac{1}{2} + \frac{3}{2}.
\]
Combining these fractions, we have:
\[
x = \frac{1 + 3}{2} = \frac{4}{2} = 2.
\]
Thus, the value of \( x \) that satisfies the equation is:
\[
\boxed{2}.
\]